E Math Tuition

Standard Form

• Convert ordinary notations into index notations such as standard form and apply the techniques onto problem sums accurately.

Linear Inequality

• Identify the inequality sign and how the signs change and its meaning.
• Draw out the various number lines correctly that represent the respective inequality and identify the final region that satisfies the inequalities.
• Work out the largest and smallest possible value from the given range of values.

Algebra

• Simplify indices and solve indices equations step by step systemically using the indices formulas.
• Solve quadratic equations confidently by completing the square and using the 3 methods.
• Solve algebra problem sums by constructing the equations logically using the variables and information provided by the question
• Solve algebra questions by simplifying and factorising algebra expression, making x the subject and solving simultaneous equation.

Graph and Coordinate Geometry

• Master the technique to form the equation of a straight line
• Understand the meaning of gradient and apply the formula to calculate the gradient of a straight line.
• Appreciate the formula for midpoint and distance and apply them confidently and correctly.
• Identify the base and height of a triangle and find the area accurately.
• Find the coordinates of a point or the intersection point between 2 lines by using the correct method.
• Sketch different types of the graphs (straight lines, quadratic curve, cubic curve, reciprocal curve, exponential curve) skilfully, indicating the critical points accurately.
• Construct a curve on the graph paper precisely using a flexible curve or french curve, showing a smooth curve with all the details clearly presented.
• Draw the gradient of tangent and apply the formula to find the gradient.
• Solve an equation graphically by simplifying the equation to be the same as the graph equation and drawing an additional straight line on the graph paper to solve the question.

Similarity and Congruency

• Identify congruent and similar triangles using the respective tests.
• Find the unknown lengths and angles in the same direction.
• Form area ratio, volume ratio and cost ratio to solve for the unknown area, volume and cost.

Circles, Arc Lengths and Area of Sector

• Appreciate the angle properties of circles and apply it correctly to find the unknown angles.
• Convert angles from degrees to radians correctly
• Appreciate the formulas of arc length and area of sectors and apply it confidently to solve for the unknown arc length and area of sectors.
• Identify right angle triangle, isosceles triangle and congruent triangle in the circle accurately presenting all the proofs in details.
• Find the unknown length with similar triangle, right angle triangle and trigo formulas.

Trigonometry

• Find the unknown length and angles in a right angle triangle using tangent, cosine and sine formulas confidently.
• Find the unknown lengths and angles in a non-right angle triangle using sine rule and cosine rule confidently.
• Draw the shortest distance from a point to a line and find the shortest distance accurately using tangent, cosine and sine formulas.
• Find the area of triangle accurately for both right angle triangle and non-right angle triangle.
• Draw the north line and bearing accurately and use trigo formulas to calculate the unknown bearing correctly.
• Solve 3D problem sums and convert parts of the 3D diagram into 2D triangle to clearly show the shortest distance, height and angle of elevation and depression. Use trigo formulas to solve for the unknown length, angles of elevation and angle of depression.

Cumulative Frequency Curve, Mean and Standard Deviation

• Mark out the lower quartile , upper quartile and the median on the cumulative frequency curve accurately and find the interquartile range.
• Use the cumulative frequency curve to find a specific frequency representing the performance above a particular score or value.
• Identify the range, lower quartile, upper quartile and median from the box and whisker plot and calculate the interquartile range.
• To find the mean, median and mode of a set of values as well as a grouped data.
• To analyse and compare the performance between 2 sets of data using mean, median, interquartile range and standard deviation.
• To analyse the impact on the mean and standard deviation triggered by a change in the data.

Probability

• To construct a possibility diagram and use it to find the probability of the occurrence of an event
• To construct a tree diagram and find the probability of the occurrence of a replacement event as well as a non-replacement event
• To identify and list out all the possible cases of an event and calculate its probability

Set Notation

• To construct the venn diagram and input all the elements in the respective sets.
• To shade the venn diagrams correctly to represent the given set notation and vice versa.
• Identify and construct all the possible venn diagrams to find the largest and smallest possible number of elements in a given set.

Speed Time graph

• Construct the distance-time graph, speed-time graph and acceleration-time graph of an object and describe its motion.
• To calculate the acceleration, speed and distance travelled by an object using the graphs.

Vectors

• Find the vector using triangle law of vector additions, ratio and similar triangle
• Find the area ratios using similar triangle, common height and the 3^rd
• Prove collinear points by showing parallel lines and a common point.
• Prove parallel vectors and calculate the magnitude of a vector.
• Convert the position vector into coordinates and vice versa.

Real World Problems

• To analyse and work out the solutions of real world questions showing all the steps clearly with logical reasonings.

Paper 1

• Reinforce and re-drill the important formulas from Sec 1 to Sec 4 topics that will be tested in Paper 1.
• Apply the correct method and show all the steps accurately to score maximum marks.